Trying to answer to Thomas' question: algorithm for the curve generation.

I hope people will not disappoint like I was when I read about Truchet tiles. I felt like when a magician explain his trick and the magic is lost.

Truchet Tiles are square tiles decorated with patterns that are not rotationally symmetric. When placed in a square tiling of the plane, they can form varied patterns.

https://en.wikipedia.org/wiki/Truchet_tiles

You choose your set of "Truchet" tiles and rotate them the way you like,while paving the wall.

I chose the Quarter-Circle tile: two quarter-circles connecting the midpoints of adjacent sides.

Usually, Truchet Tiles are on a plane! I wanted to tile on a surface. As far as a curvilinear coordinate ( U V) system can be used for a surface, you can feel safe.

Algorithm 

1. Divide surface (by its U and V) -> you got the pavement and tile system

2. for each tile of the pavement

• get the list of edges (4 edges) 
• Shift the list of 0 or 1 randomly

3. for each edges

• Get mid point
• create a segment orthogonal to the edge toward the exterior of the tile

4. create a connect curve between point 1 and 2 of the tile and tangent to the segments of step3

5. create a connect curve between point 3 and 4 of the tile and tangent to the segments of step3

6. circle sweep the curves

Issues / Modeling tricks

• to set a direction toward the exterior of the tiles, I had to use a condition, Dispatch-End Dispatch.
• I could not use Divide function on a Torus. I had to split the Torus into 2. This will be reported to R&D

Next Try

• Hexagonal tiling instead of square tiling.

Request

• Longer weekends...